Average Error: 0.0 → 0.0
Time: 4.2s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\sqrt[3]{{\left({\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}\right)}^{3}}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\sqrt[3]{{\left({\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}\right)}^{3}}}
double f(double f, double n) {
        double r17869 = f;
        double r17870 = n;
        double r17871 = r17869 + r17870;
        double r17872 = -r17871;
        double r17873 = r17869 - r17870;
        double r17874 = r17872 / r17873;
        return r17874;
}
↓
double f(double f, double n) {
        double r17875 = f;
        double r17876 = n;
        double r17877 = r17875 + r17876;
        double r17878 = -r17877;
        double r17879 = r17875 - r17876;
        double r17880 = r17878 / r17879;
        double r17881 = 3.0;
        double r17882 = pow(r17880, r17881);
        double r17883 = pow(r17882, r17881);
        double r17884 = cbrt(r17883);
        double r17885 = cbrt(r17884);
        return r17885;
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube41.2

    \[\leadsto \frac{-\left(f + n\right)}{\color{blue}{\sqrt[3]{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}\]

  4. Applied add-cbrt-cube42.0

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(-\left(f + n\right)\right) \cdot \left(-\left(f + n\right)\right)\right) \cdot \left(-\left(f + n\right)\right)}}}{\sqrt[3]{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}\]

  5. Applied cbrt-undiv42.0

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(-\left(f + n\right)\right) \cdot \left(-\left(f + n\right)\right)\right) \cdot \left(-\left(f + n\right)\right)}{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}\]

  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube0.0

    \[\leadsto \sqrt[3]{\color{blue}{\sqrt[3]{\left({\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3} \cdot {\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}\right) \cdot {\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}}\]

  9. Simplified0.0

    \[\leadsto \sqrt[3]{\sqrt[3]{\color{blue}{{\left({\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}\right)}^{3}}}}\]

  10. Final simplification0.0

    \[\leadsto \sqrt[3]{\sqrt[3]{{\left({\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))